Helfrich cylinders -- instabilities, bifurcations and amplitude equations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911095585767424 |
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| author | Meiners, Alexander Uecker, Hannes |
| author_facet | Meiners, Alexander Uecker, Hannes |
| contents | Combining local bifurcation analysis with numerical continuation and bifurcation methods we study bifurcations from cylindrical vesicles described by the Helfrich equation with volume and area constraints, with a prescribed periodicity along the cylindrical axis. The bifurcating solutions are in two main classes, axisymmetric (pearling), and non-axisymmetric (coiling, buckling, and wrinkling), and depending on the spontaneous curvature and the prescribed periodicity along the cylinder axis we obtain different stabilities of the bifurcating branches, and different secondary bifurcations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_21137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Helfrich cylinders -- instabilities, bifurcations and amplitude equations Meiners, Alexander Uecker, Hannes Analysis of PDEs 35B32, 58J55, 65P30 Combining local bifurcation analysis with numerical continuation and bifurcation methods we study bifurcations from cylindrical vesicles described by the Helfrich equation with volume and area constraints, with a prescribed periodicity along the cylindrical axis. The bifurcating solutions are in two main classes, axisymmetric (pearling), and non-axisymmetric (coiling, buckling, and wrinkling), and depending on the spontaneous curvature and the prescribed periodicity along the cylinder axis we obtain different stabilities of the bifurcating branches, and different secondary bifurcations. |
| title | Helfrich cylinders -- instabilities, bifurcations and amplitude equations |
| topic | Analysis of PDEs 35B32, 58J55, 65P30 |
| url | https://arxiv.org/abs/2502.21137 |